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Simple Quadratic Forms Read chapter Read first chapter

2018 | OriginalPaper | Chapter

6. Two of Gauss’s Proofs of Quadratic Reciprocity

Author : Jeremy Gray

Published in: A History of Abstract Algebra

Publisher: Springer International Publishing

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Abstract

In this chapter, we discuss two of Gauss’s proofs of quadratic reciprocity: one (his second) uses composition of forms, and the other (his sixth) uses cyclotomy. The sixth was the last proof of this theorem he published, although he went on to leave two more unpublished.

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previous chapter Cyclotomy
next chapter Dirichlet’s Lectures on Quadratic Forms
Footnotes
1
Recall that a form (a, b, c) is properly primitive if the greatest common divisor of a,  2b, c is 1.
 
2
For a translation of Gauss’s sixth proof, see Appendix C.
 
3
This profusion of footnotes tells us that there was a priority dispute between these men, all of whom were in any case following Gauss.
 
Literature
Lemmermeyer, F.: Reciprocity Laws. From Euler to Eisenstein. Springer Monographs in Mathematics, Springer, Berlin (2000)
Scharlau, W., Opolka, H.: From Fermat to Minkowski. Springer, Berlin (1984)MATH
Metadata
Title
Two of Gauss’s Proofs of Quadratic Reciprocity
Author
Jeremy Gray
Copyright Year
2018
Book
A History of Abstract Algebra

Print ISBN: 978-3-319-94772-3

Electronic ISBN: 978-3-319-94773-0

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-94773-0_6

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